Conservation of Angular momentum and 3D circular motion

Fu-Kwun Hwang

Administrator
Hero Member

Offline

Posts: 3082

1 Conservation of Angular momentum and 3D circular motion

Embed this message

on: March 12, 2010, 11:06:08 pm » posted from:Taipei,T\'ai-pei,Taiwan

A particle with mass $m$ is moving with constant speed $v$ along a circular orbit (radius $r$ ).
The centripetal force $F=m\frac{v^2}{r}$ is provided by gravitation force from another mass $M=F/g$ .
A string is connected from mass m to the origin then connected to mass $M$ .
Because the force is always in the $\hat{r}$ direction, so the angular momentum $\vec{L}=m\,\vec{r}\times \vec{v}$ is conserved. i.e. $L=mr^2\omega$ is a constant.

For particle with mass m:

$m \frac{d^2r}{dt^2}=m\frac{dv}{dt}= m \frac{v^2}{r}-Mg=\frac{L^2}{mr^3}- Mg$
$\omega=\frac{L}{mr^2}$

The following is a simulation of the above model.

You can change the mass M or the radius r with sliders.
The mass M also changed to keep the mass m in circular motion when you change r.
However, if you change mass M , the equilibrium condition will be broken.

Embed a running copy of this simulation

Embed a running copy link(show simulation in a popuped window)

Full screen applet or Problem viewing java?Add http://www.phy.ntnu.edu.tw/ to exception site list
Press the Alt key and the left mouse button to drag the applet off the browser and onto the desktop. This work is licensed under a Creative Commons Attribution 2.5 Taiwan License

Please feel free to post your ideas about how to use the simulation for better teaching and learning.
Post questions to be asked to help students to think, to explore.
Upload worksheets as attached files to share with more users.

Let's work together. We can help more users understand physics conceptually and enjoy the fun of learning physics!

circular3dfr.gif (4.01 KB, 508x418 - viewed 773 times.)
	Logged

macfamous

watchlist
Newbie

Offline

Posts: 5

2 Re: Conservation of Angular momentum and 3D circular motion

Embed this message

Reply #1 on: March 19, 2010, 10:53:15 am » posted from:Yogyakarta,Yogyakarta,Indonesia

there is more simple formula for this simulation Huh


	Logged

Fu-Kwun Hwang

Administrator
Hero Member

Offline

Posts: 3082

3 Re: Conservation of Angular momentum and 3D circular motion

Embed this message

Reply #2 on: March 19, 2010, 01:22:45 pm » posted from:Taipei,T\'ai-pei,Taiwan

Quote

there is more simple formula for this simulation

Could you explain what do you mean in detail?


	Logged

lookang

Hero Member

Offline

Posts: 1792

http://weelookang.blogspot.com

4 Re: Conservation of Angular momentum and 3D circular motion

Embed this message

Reply #3 on: July 07, 2010, 12:32:23 pm » posted from:SINGAPORE,SINGAPORE,SINGAPORE

question:
how is the tension in the string calculated?

My understanding:
T = m*v*v/r; // added lookang for tension only work for circular motion

my hypothesis:
T1 = m*v*v/r + m*dvr/dt ? // radial acceleration due to tangential change in velocity and radial acceleration due to radial change in velocity ?

where dvr/dt = (cst*cst/(m*r*r*r)-M*g)/m

My equation:
T1 = m*v*v/r +(cst*cst/(m*r*r*r)-M*g) ;
can help take a look if my equation of Tension is correct ?
did i get the generalized equation for tension in any elliptical motion?
the logic seems correct and i implement the equation looks correct. is it correct conceptually in the absence of frictional forces

* There are 1 more attached files. You need to login to acces it!**
« Last Edit: July 07, 2010, 12:54:54 pm by lookang »	Logged

Fu-Kwun Hwang

Administrator
Hero Member

Offline

Posts: 3082

5 Re: Conservation of Angular momentum and 3D circular motion

Embed this message

Reply #4 on: July 07, 2010, 06:05:49 pm » posted from:Taipei,T\'ai-pei,Taiwan

If the mass is in circular motion, then the tension $T=m\frac{v^2}{r}$ .

What if we increase the tension so that $T>m\frac{v^2}{r}$ .
Will the mass moving inward( $\frac{dv_r}{dt}<0$ ) or moving outward( $\frac{dv_r}{dt}>0$ )?

Thank about it and then check with your equation!


	Logged

lookang

Hero Member

Offline

Posts: 1792

http://weelookang.blogspot.com

6 Re: Conservation of Angular momentum and 3D circular motion

Embed this message

Reply #5 on: July 07, 2010, 06:16:08 pm »

Quote from: Fu-Kwun Hwang on July 07, 2010, 06:05:49 pm

I see I got the sign convention wrong!
I forgot the convention for r unit vector is positive outward.
Will change it to
T1 = m*v*v/r -(cst*cst/(m*r*r*r)-M*g) ;
thanks !!!

your masterful questioning allows to think and figure out the answer myself.
Appreciate your superb advise

my remixed applet is here
http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=1883.0
enjoy!


« Last Edit: July 07, 2010, 06:21:45 pm by lookang »	Logged

Pages: [1] Go Up

"Choose a job you love, and you will not have to work for a day in your life." ...Confucius (551-479 BC)

« previous next »

Related Topics
	Subject	Started by	Replies	Views	Last post
	Angular momentum and Area kinematics	Fu-Kwun Hwang	10	85716	November 23, 2007, 04:48:20 pm by Fu-Kwun Hwang
	Conservation of momentum Molecular Workbench	concord	0	8999	December 23, 2007, 06:45:41 am by concord
	Angular momentum of a sphere Kinematics	Fu-Kwun Hwang	0	15682	July 05, 2009, 09:28:21 pm by Fu-Kwun Hwang
	Conservation of Angular momentum and 3D circular motion dynamics	ahmedelshfie	0	5145	April 15, 2010, 01:06:20 am by ahmedelshfie
	Wheel , angular momentum, torque Dynamics	Fu-Kwun Hwang	1	4727	April 09, 2013, 10:45:19 pm by Fu-Kwun Hwang

	Author	Topic: Conservation of Angular momentum and 3D circular motion (Read 17756 times)
0 Members and 1 Guest are viewing this topic. Click to toggle author information(expand message area).